Nonlocal Ginzburg–Landau theory for superconductors

The conventional Ginzburg–Landau (GL) theory is extended to a nonlocal one. In this nonlocal GL theory the superconducting current becomes nonlocal. The magnetic field distribution calculated in the single vortex state indicates that the interaction between vortices has an attractive part in low-κ type II superconductors with κ < κc ∼ 1. The attractive interaction causes the first-order transition at Hc1.

► Nonlocal GL theory is proposed, which contains a nonlocal gradient term.
► The superconducting current has a nonlocal form in this theory.
► Nonlocal GL theory can describe the attractive interaction between vortices.